Abstract

The solution of the linearized Ginzburg-Landau theory describing a periodic lattice of vortex lines in type-II superconductors with high inductions and first discovered by Abrikosov is generalized to nonperiodic vortex arrangements, e.g. lattices with a vacancy, surrounded by a relaxing vortex lattice, and periodically distorted lattices that are needed in the nonlocal theory of elasticity of a vortex lattice. Generalizations to lower magnetic inductions and three-dimensional arrangements of curved vortex lines are also given. It is shown how a periodic vortex lattice can be computed for bulk superconductors and for thick and thin films in a perpendicular field for all inductions and all Ginzburg-Landau parameters .